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arXiv · 1411.0046

The Dispersion Relation for Matter Waves in a Two-Phase Vacuum

Paul S. Wesson
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Abstract

The cosmological constant (lambda) of general relativity is a natural consequence of embedding Einstein's theory in a five-dimensional theory of the type needed for unification. The exact 5D solution for lambda less than 0 shows waves in ordinary 3D space with properties similar to those of de Broglie or matter waves. Here the dispersion relation is derived for matter waves in a toy two-phase model, where regions with lambda less than 0 and lambda greater than 0 average on the large scale to lambda = 0, thus providing in principle a resolution of the cosmological-constant problem. A striking result of the analysis is that the dispersion relation is bimodal, with a well-defined window of high-frequency transmission which effectively defines the speed of light.

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Paul S. Wesson. 2014-11-01. The Dispersion Relation for Matter Waves in a Two-Phase Vacuum. https://doi.org/10.1142/s0217732314501685

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